Electrical Circuits Summary

Charge

• Charge is a physical property causing force in an electric field.

  • Positive (e.g., protons).

  • Negative (e.g., electrons).

• Protons and neutrons are tightly bound in the nucleus.

• Electrons are loosely bound in an electron cloud.

• Ions are charged atoms:

  • Positive ions have lost electrons.

  • Negative ions have gained electrons.

Coulomb

• Charge is measured in Coulombs (C).

• $1 C = 6.24 x 10^{18} q_e$

• Elementary charge ($q<em>e$) is the charge of a single proton ($+q</em>e$) or electron ($-q_e$).

  • Proton: $+q_e = +1.6 x 10^{-19} C$

  • Electron: $-q_e = -1.6 x 10^{-19} C$

Law of Conservation of Charge

• Frictional charging involves electron transfer.

• Net charge lost by one object is gained by the other.

• The law states that the net charge produced in any transfer process is 0.

  • Charge before = Charge after.

Conductors and Insulators

• Conductors allow free movement of charge.

  • Examples: metals, sodium chloride solution.

  • Charge spreads over the surface.

• Insulators restrict charge movement.

  • Examples: wood, rubber, plastic, glass.

  • Charge stays in place.

Current and Electron Flow

• Electric current is the rate of motion of charge carriers.

  • Symbol: I, Units: Amperes (A)

• $I = q/t$ where q is charge in coulombs and t is time in seconds.

• 1 Amp = 1 Coulomb / second.

• Direct Current (DC): Charge flows in one direction (e.g., batteries).

• Alternating Current (AC): Charge flow varies in magnitude and direction (e.g., household electricity).

Open and Closed Circuits

• Closed circuit: continuous path for charge flow (switch is on).

• Open circuit: interrupted path, no charge flow (switch is off).

Electrical Potential

• Electric potential is the work needed to move a unit charge (1 C) from one point to another; the electrical potential energy per unit of charge.

• Symbol: V, Unit: Volt (V).

Electric Potential Difference

• The change in potential energy per unit charge between two points.

• Unit: Volt (V), also referred to as Voltage.

Sources of Electrical Potential

• Battery (cell): Metals separated by conducting solutions.

• Electromotive Force (EMF): Potential difference that causes electric current.

Power

• Power is the rate at which work is done or energy is transferred.

• Units: Watts (W).

• $P = W/t$

• Using current, I = q/t:

  • $P = IV$

Resistance

• Electrical resistance opposes current flow.

  • Units: Ohms (Ω)

Factors Affecting Resistance

• Length (L): Resistance is directly proportional to length.

• Cross-sectional Area (A): Resistance is inversely proportional to area.

• Material: Different materials have different resistance due to their atomic lattice.

Ohm's Law

• Current through a resistance wire is proportional to the voltage across it (at constant temperature).

• $V = IR$

• $R = V/I$

Ohmic vs. Non-Ohmic Resistors

• Ohmic: Follow Ohm's Law (linear relationship between voltage and current).

• Non-Ohmic: Do not follow Ohm's Law.

Resistors in Series

• Equivalent resistance is the sum of individual resistances: $R<em>{eq} = R</em>1 + R_2 + …$

• Same current flows through each resistor.

• Potential difference (voltage) varies across each resistor.

Resistors in Parallel

• The total (equivalent) resistance is found using $1/R<em>{eq} = 1/R</em>1 + 1/R_2 + …$

• Each resistor has the same full voltage of the source applied to it.

• Current across each resistor varies; calculate using $I = V/R$

Kirchhoff’s Current Law

• Electric charge is conserved at all points in a circuit.

• Total current flowing into a node equals the total current flowing out: $I<em>{in} = I</em>{out}$

Kirchhoff’s Voltage Law

• The total voltage in a closed circuit is the sum of all the voltages:

• $V<em>T = V</em>1 + V<em>2 + … + V</em>n$

Standard Electrical Symbols

• Cell, Battery, Switch, Resistor, Voltmeter, Ammeter, Light Bulb

Power Dissipation

• The rate at which energy is lost in an electrical system.

• Unit: kWh (kilowatt-hour), the number of watts used in an hour.

• $P = IV$